Abstract

The least squares grid-free method, though having the ability to work effectively on any distribution of points is limited by the requirement of a good connectivity around a node. This paper deals with a fundamental improvement over the usual least squares grid-free method to overcome this limitation of the grid-free method. The new approach involves the use of the weights to diagonalize the least squares matrix A such that the x and y directions become the eigen directions along which the higher dimensional least squares formulae reduce to the one dimensional formulae. A very important advantage of this approach (apart from improving the convergence characteristics of the grid-free solver) is that it helps in tackling the problems of code divergence due to the degenerate and other cases of bad connectivity.